Problem: Nauuo is a girl who loves playing chess.

One day she invented a game by herself which needs n chess pieces to play on a m× m chessboard. The rows and columns are numbered from 1 to m. We denote a cell on the intersection of the r-th row and c-th column as (r,c).

The game's goal is to place n chess pieces numbered from 1 to n on the chessboard, the i-th piece lies on (r_i,\,c_i), while the following rule is satisfied: for all pairs of pieces i and j, |r_i-r_j|+|c_i-c_j|≥|i-j|. Here |x| means the absolute value of x.

However, Nauuo discovered that sometimes she couldn't find a solution because the chessboard was too small.

She wants to find the smallest chessboard on which she can put n pieces according to the rules.

She also wonders how to place the pieces on such a chessboard. Can you help her?

Input

The only line contains a single integer n (1≤ n≤ 1000) — the number of chess pieces for the game.

Output

The first line contains a single integer — the minimum value of m, where m is the length of sides of the suitable chessboard.

The i-th of the next n lines contains two integers r_i and c_i (1≤ r_i,c_i≤ m) — the coordinates of the i-th chess piece.

If there are multiple answers, print any.

Examples

Input


2


Output


2
1 1
1 2

Input


4


Output


3
1 1
1 3
3 1
3 3

Note

In the first example, you can't place the two pieces on a 1×1 chessboard without breaking the rule. But you can place two pieces on a 2×2 chessboard like this:

<image>

In the second example, you can't place four pieces on a 2×2 chessboard without breaking the rule. For example, if you place the pieces like this:

<image>

then |r_1-r_3|+|c_1-c_3|=|1-2|+|1-1|=1, |1-3|=2, 1<2; and |r_1-r_4|+|c_1-c_4|=|1-2|+|1-2|=2, |1-4|=3, 2<3. It doesn't satisfy the rule.

However, on a 3×3 chessboard, you can place four pieces like this:

<image>

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public class Solution{
    
    public static void main(String[] args) throws Exception{
        int n = in.readInt();

        int m = (n)/2 + 1;
        int[][] coord = new int[n+1][2];
        int t = 1;
        int x = 1, y = 1, rx = m, ry = m;
        while(t <= (n+1)/2){
            int px = x, prx = rx;
            while(x <= m && y > 0 && t <= (n+1)/2){
                coord[t] = new int[]{x,y};
                coord[n-t+1] = new int[]{rx,ry};
                x++;    y--;
                rx++;   ry--;
                t++;
            }
            x = px+1;    y=1;
            rx = prx-1;   ry=m;   
        }

        System.out.println(m);
        for(int i = 1; i <= n; i++){
            System.out.println(coord[i][0]+" "+coord[i][1]);
        }
    }

    static Inputer in;
    static {
        in = new Inputer();
    }

    static class Inputer{
        BufferedReader br;
        Inputer(){
            try{
                br = new BufferedReader(new InputStreamReader(System.in));
            }
            catch(Exception e){}
        }
        public int readInt() throws Exception{
            return Integer.parseInt(readLine());
        }
        public long readLong() throws Exception{
            return Long.parseLong(readLine());
        }
        public int[] readA(String delim) throws Exception{
            String[] s = readLine().split(delim);
            int[] A = new int[s.length];
            for(int i = 0; i < s.length; i++)
                A[i] = Integer.parseInt(s[i]);
            return A;
        }
        public int[] readA() throws Exception{
            String[] s = readLine().split("\\s+");
            int[] A = new int[s.length];
            for(int i = 0; i < s.length; i++)
                A[i] = Integer.parseInt(s[i]);
            return A;
        }
        public long[] readLA() throws Exception{
            String[] s = readLine().split("\\s+");
            long[] A = new long[s.length];
            for(int i = 0; i < s.length; i++)
                A[i] = Long.parseLong(s[i]);
            return A;
        }
        public String readLine() throws Exception{
            return br.readLine();
        }
        public int[] copyA(int[] A){
            int[] B = new int[A.length];
            for(int i= 0 ; i < A.length; i++)
                B[i] = A[i];
            return B;
        }
    }
}